Minimality of p-adic rational maps with good reduction

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成果类型：

期刊论文

作者：

Fan, Aihua;Fan, Shilei*;Liao, Lingmin;Wang, Yuefei

通讯作者：

Fan, Shilei

作者机构：

[Fan, Aihua; Fan, Shilei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.

[Fan, Aihua] Univ Picardie Jules Verne, CNRS, LAMFA, UMR 7352, 33 Rue St Leu, F-80039 Amiens 1, France.

[Fan, Shilei] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.

[Liao, Lingmin] Univ Paris Est Creteil, LAMA, UMR 8050, CNRS, 61 Ave Gen Gaulle, F-94010 Creteil, France.

[Wang, Yuefei] Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China.

通讯机构：

[Fan, Shilei] C

Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.

Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.

语种：

英文

关键词：

$p$-adic dynamical system;minimal decomposition;projective line;good reduction;rational map

期刊：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

ISSN：

1078-0947

年：

2017

卷：

期：

页码：

3161-3182

DOI：

10.3934/dcds.2017135

基金类别：

A. H. FAN was supported by NSF of China (Grant No. 11471132); S. L. FAN was supported by NSF of China (Grant No. 11401236) and self-determined research funds of CCNU (Grant No. CCNU17QN0009); Y. F. WANG was supported by NSF of China (Grant No. 11231009)

机构署名：

本校为第一且通讯机构

院系归属：

数学与统计学学院

摘要：

A rational map with good reduction in the field ℚp of p-adic numbers defines a 1-Lipschitz dynamical system on the projective line ℙ1(ℚp) over ℚp. The dynamical structure of such a system is completely described by a minimal decomposition. That is to say, ℙ1 (ℚp) is decomposed into three parts: Finitely many periodic orbits; finite or countably many minimal subsystems each consisting of a finite union of balls; and the attracting basins of periodic orbits and minimal subsystems. For any prime p, a criterion of minimality for rational maps...

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Minimality of p-adic rational maps with good reduction

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